6.2 Limitations 125 framework of LSBD as a particular paradigm for learning better representations, our final set of research questions focuses on how well LSBD models can learn to capture the underlying mechanisms of the data, such that they can generalise to unseen data that is the result of these same mechanisms. We formulate this as out-of-distribution (OOD) generalisation, or more specifically combinatorial generalisation. The idea is that certain combinations of underlying factors may not be observed due to factor correlations or limited data observations, but these combinations should still be considered normal since they are the result of the mechanisms we aim to model with LSBD. Previous work has investigated how well traditional disentanglement models perform in such OOD generalisation settings (Montero et al., 2021; Schott et al., 2022), concluding somewhat surprisingly that these models struggle to generalise the learned disentangled factors to unseen (i.e. OOD) combinations. In Chapter 5, we evaluate the performance of LSBD-VAE as well as traditional disentanglement models on a number of OOD generalisation settings. Results show that both LSBD and traditional disentanglement models struggle to generalise in more challenging settings, and that overall LSBD shows no improvement in generalisation when measured in terms of the likelihood of the OOD data. However, upon more closely inspecting the way data gets encoded into representations, we observe that LSBD-VAE can still obtain equivariant representations even for the OOD data. This suggests that the encoder still generalises fairly well to such OOD data, even if the decoder struggles to accurately reconstruct such data points. To conclude, our findings indicate that both LSBD models and traditional disentanglement models fail to deliver on their promise to generalise well to OOD combinations, and that there remains work to be done to learn disentangled models that accurately represent the disentangled factors outside of the observed data distribution. However, it is promising to see that LSBD models do seem to learn how to encode decently equivariant representations for unobserved factor combinations, even if they struggle to reconstruct such combinations into a plausible generated data point. 6.2 Limitations The anomaly detection results from Chapter 3 showcase the suitability of deep generative models, in particular VAEs, to perform anomaly detection by learning a likelihood model of normal, non-anomalous data. However, this limits our work to settings where it is feasible to obtain a dataset of normal samples, i.e.
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